State-Dependent Impulses Boundary Value Problems on Compact Interval /

• Main Authors: Rachůnková, Irena (Author), Tomeček, Jan (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Paris : Atlantis Press : Imprint: Atlantis Press, 2015.
• Edition: 1st ed. 2015.
• Series: Atlantis Briefs in Differential Equations, 6
• Subjects: Mathematics.; Differential equations.; Ordinary Differential Equations.
• Physical Description: XV, 190 p. 7 illus. online resource.
• ISBN: 9789462391277
• ISSN: 2405-6405 ;

This book offers the reader a new approach to the solvability of boundary value problems with state-dependent impulses and provides recently obtained existence results for state dependent impulsive problems with general linear boundary conditions. It covers fixed-time impulsive boundary value problems both regular and singular and deals with higher order differential equations or with systems that are subject to general linear boundary conditions. We treat state-dependent impulsive boundary value problems, including a new approach giving effective conditions for the solvability of the Dirichlet problem with one state-dependent impulse condition and we show that the depicted approach can be extended to problems with a finite number of state-dependent impulses. We investigate the Sturm–Liouville boundary value problem for a more general right-hand side of a differential equation. Finally, we offer generalizations to higher order differential equations or differential systems subject to general linear boundary conditions.